Question: Simplify to lowest terms. $\dfrac{56}{70}$
There are several ways to tackle this problem. What is the greatest common factor (GCD) of 56 and 70? $56 = 2\cdot2\cdot2\cdot7$ $70 = 2\cdot5\cdot7$ $\mbox{GCD}(56, 70) = 2\cdot7 = 14$ $\dfrac{56}{70} = \dfrac{4 \cdot 14}{ 5\cdot 14}$ $\hphantom{\dfrac{56}{70}} = \dfrac{4}{5} \cdot \dfrac{14}{14}$ $\hphantom{\dfrac{56}{70}} = \dfrac{4}{5} \cdot 1$ $\hphantom{\dfrac{56}{70}} = \dfrac{4}{5}$ You can also solve this problem by repeatedly breaking the numerator and denominator into common factors. For example: $\dfrac{56}{70}= \dfrac{2\cdot28}{2\cdot35}= \dfrac{2\cdot 7\cdot4}{2\cdot 7\cdot5}= \dfrac{4}{5}$